Is this meaning "It is not available at this moment." Or "It is not available any more."?
Only the former.
what would "he is not available now"? I'm just a little confused on the "se".
The "sé" is usually (and in this case as well) totally interchangeable, either "he" or "it". The context decides which is the intended use.
Why not "It is not currently available"?
That sounds to me more like "faoi láthair". (https://www.teanglann.ie/en/eid/Currently)